arXiv subjects

Jiaxin Xie

Publications and source records attributed to Jiaxin Xie.

At least 19 recordsLinked to original sources

arXiv2026

HappyWorld-Bench

Evaluating world models requires assessing both the quality of the worlds they generate and their consistency and responsiveness under exploration, interaction, and modification. We introduce HappyWorld-Bench, a comprehensive benchmark that evaluates whether generated worlds remain reliable as agents interact with them. Our design is built on a hierarchical capability framework of six world capabilities (W1-W6), from generative construction to unified world modeling, instantiated across three independent evaluation tracks: video world models, spatial world models, and embodied world models. HappyWorld-Bench comprises 1,138 video prompts, 300 spatial scenes, and 254 embodied test cases. Across all three tracks, we build and operate HappyWorld-Arena to organize human A/B comparisons and derive model-level Elo ratings, which complement newly designed automated metrics that capture behavioral correctness. We evaluate 14 video world models, 9 spatial systems, and 8 embodied candidates under this unified framework. Results reveal remaining reliability gaps across all three tracks: video models exhibit reduced consistency during extended rollouts and revisits, spatial models achieve at best 70.14% placement accuracy and 73.33% edit execution, and embodied models struggle to preserve state across multi-step actions and respond precisely to altered action conditions and physical rules. These findings highlight the need to evaluate world models not only by visual quality, but also by state consistency and the correctness of their responses to actions and interventions.

cs.CV↗

arXiv2026

Projecting onto the unit dual quaternion set

Dual quaternions have gained significant attention due to their wide applications in areas such as multi-agent formation control, 3D motion modeling, and robotics. A fundamental aspect in dual quaternion research involves the projection onto the unit dual quaternion set. In this paper, we systematically study such projections under the $2^R$-norm, which is commonly used in practical applications. We identify several distinct cases based on the relationship between the standard and dual parts in vector form, and demonstrate the effectiveness of the proposed algorithm through numerical experiments.

math.NA↗

arXiv2026

Randomized iterative methods with Polyak step-size for solving generalized absolute value equations

In this paper, we systematically incorporate the Polyak step-size into the randomized iterative method to improve its efficiency for solving generalized absolute value equations. In particular, we adopt the Polyak step-size within a stochastic iterative setting where the objective function updates dynamically at every step, unlike the classical Polyak step-size designed for deterministic optimization with fixed objective functions. Consequently, this novel implementation differs from the conventional Polyak scheme and demands a dedicated convergence analysis. We rigorously analyze the convergence properties of the proposed method and establish its linear convergence in expectation. Numerical experiments demonstrate that the incorporation of the Polyak step-size substantially improves the computational performance of randomized iterative methods with constant step-sizes.

math.NA↗

arXiv2026

ICDepth: Taming Video Diffusion Models for Video Depth Estimation via In-Context Conditioning

Monocular video depth estimation requires temporal consistency, geometric accuracy, and generalization across diverse scenarios, yet existing methods struggle to achieve all three simultaneously. Discriminative models excel at per-frame accuracy but suffer from temporal drift due to limited context windows, while generative methods improve consistency and generalization at the cost of extensive training data (10M+ samples) and lack of geometric precision. In response to these issues, we introduce \textbf{ICDepth}, a framework that adapts pre-trained text-to-video diffusion transformers for video depth estimation via In-Context Conditioning (ICC), leveraging their rich spatial-temporal priors. To address key challenges in transferring ICC from generation to dense prediction, we propose: (1)~\textbf{SAND-Attention}, which ensures precise spatial-temporal alignment via shared RoPE and enforces unidirectional attention to prevent noise contamination; (2)~\textbf{SRFM}, which injects DINOv2 semantic and resolution priors to enhance geometric precision. ICDepth achieves state-of-the-art results on multiple benchmarks with remarkable data efficiency, trained on only 0.8M frames ($6$--$13\times$ less than competing generative methods), while demonstrating strong zero-shot generalization to diverse domains.

cs.CV↗

arXiv2026

On subspace-constrained preconditioning for randomized iterative methods

In this paper, we further investigate and refine the subspace-constrained preconditioning technique to enhance the theoretical and numerical convergence properties of randomized iterative methods for solving linear systems. In particular, we design a QR-like factorization that transforms the original linear system into an equivalent block-orthogonal form, thus avoiding the full-rank assumptions adopted in existing work. Moreover, this reformulation reduces the problem to solving a smaller linear system with a favorable singular value distribution, provided an appropriate initial point is employed. The proposed framework can be implemented implicitly within the iteration and does not require explicitly constructing either a preconditioner matrix or a preconditioned linear system, which eliminates the prohibitive cost of forming a fully preconditioned system. Furthermore, we construct orthogonalized search directions from stochastic gradients and develop accelerated variants of the framework. We prove that the proposed algorithmic framework converges linearly in expectation. Numerical experiments demonstrate the benefits of the proposed preconditioning strategy.

math.NA↗

arXiv2026

Randomized conjugate gradient least squares

We develop a novel randomized conjugate gradient least squares (RCGLS) method for solving least-squares problems, in which iterative sketching is employed at each step to reduce the dimension and hence the computational cost. In particular, we propose a new perspective on the classical CGLS method, where the next descent direction is determined via a constraint correction problem associated with the gradient. Based on this insight, we replace the gradient with a randomized coordinate gradient that naturally satisfies the variance reduction property, leading directly to the proposed RCGLS method. We prove that RCGLS converges linearly in expectation, with a better convergence bound compared to the randomized coordinate descent method. Furthermore, we investigate an implementation of the method that avoids full-dimensional vector operations, which are the major bottleneck of vanilla RCGLS for sparse matrices and render it impractical. We also show how to apply the RCGLS method to solve the ridge regression problem, yielding a lightweight, parallelizable, and accelerated method for such problems. Numerical experiments are provided to confirm our results.

math.NA↗

arXiv2026

Linear convergence of Gearhart-Koshy accelerated Kaczmarz methods for tensor linear systems

The generalized Gearhart-Koshy acceleration is a recent exact affine search technique designed for the method of cyclic projections onto hyperplanes, i.e., the Kaczmarz method. However, its convergence properties, particularly the linear convergence rate, have not been thoroughly established. In this paper, we systematically establish the linear convergence of the generalized Gearhart-Koshy accelerated Kaczmarz method for tensor linear systems, proving that it converges linearly to the unique least-norm solution. Our analysis is general and applies to several popular Kaczmarz variants, including incremental, shuffle-once, and random-reshuffling schemes, and demonstrates that this acceleration approach yields a better convergence upper bound compared to the plain Kaczmarz method. We also propose an efficient Gram-Schmidt-based implementation that computes the next iterate in linear time. Building on this implementation, we establish a connection between this acceleration framework and Arnoldi-type Krylov subspace methods, further highlighting its efficiency and potential. Our theoretical results are supported by numerical experiments.

math.NA↗

arXiv2026

Stochastic dual coordinate descent with adaptive heavy ball momentum for linearly constrained convex optimization

The problem of finding a solution to the linear system $Ax = b$ with certain minimization properties arises in numerous scientific and engineering areas. In the era of big data, the stochastic optimization algorithms become increasingly significant due to their scalability for problems of unprecedented size. This paper focuses on the problem of minimizing a strongly convex function subject to linear constraints. We consider the dual formulation of this problem and adopt the stochastic coordinate descent to solve it. The proposed algorithmic framework, called adaptive stochastic dual coordinate descent, utilizes sampling matrices sampled from user-defined distributions to extract gradient information. Moreover, it employs Polyak's heavy ball momentum acceleration with adaptive parameters learned through iterations, overcoming the limitation of the heavy ball momentum method that it requires prior knowledge of certain parameters, such as the singular values of a matrix. With these extensions, the framework is able to recover many well-known methods in the context, including the randomized sparse Kaczmarz method, the randomized regularized Kaczmarz method, the linearized Bregman iteration, and a variant of the conjugate gradient (CG) method. Additionally, we introduce an equivalent formulation that, in certain cases, substantially reduces the need for full-dimensional vector operations introduced by the momentum term. We prove that, with strongly admissible objective function, the proposed method converges linearly in expectation. Numerical experiments are provided to confirm our results.

math.NA↗

arXiv2025

Pan-LUT: Efficient Pan-sharpening via Learnable Look-Up Tables

Recently, deep learning-based pan-sharpening algorithms have achieved notable advancements over traditional methods. However, deep learning-based methods incur substantial computational overhead during inference, especially with large images. This excessive computational demand limits the applicability of these methods in real-world scenarios, particularly in the absence of dedicated computing devices such as GPUs and TPUs. To address these challenges, we propose Pan-LUT, a novel learnable look-up table (LUT) framework for pan-sharpening that strikes a balance between performance and computational efficiency for large remote sensing images. Our method makes it possible to process 15K*15K remote sensing images on a 24GB GPU. To finely control the spectral transformation, we devise the PAN-guided look-up table (PGLUT) for channel-wise spectral mapping. To effectively capture fine-grained spatial details, we introduce the spatial details look-up table (SDLUT). Furthermore, to adaptively aggregate channel information for generating high-resolution multispectral images, we design an adaptive output look-up table (AOLUT). Our model contains fewer than 700K parameters and processes a 9K*9K image in under 1 ms using one RTX 2080 Ti GPU, demonstrating significantly faster performance compared to other methods. Experiments reveal that Pan-LUT efficiently processes large remote sensing images in a lightweight manner, bridging the gap to real-world applications. Furthermore, our model surpasses SOTA methods in full-resolution scenes under real-world conditions, highlighting its effectiveness and efficiency.

cs.CV↗

arXiv2025

On adaptive stochastic extended iterative methods for solving least squares

In this paper, we propose a novel adaptive stochastic extended iterative method, which can be viewed as an improved extension of the randomized extended Kaczmarz (REK) method, for finding the unique minimum Euclidean norm least-squares solution of a given linear system. In particular, we introduce three equivalent stochastic reformulations of the linear least-squares problem: stochastic unconstrained and constrained optimization problems, and the stochastic multiobjective optimization problem. We then alternately employ the adaptive variants of the stochastic heavy ball momentum (SHBM) method, which utilize iterative information to update the parameters, to solve the stochastic reformulations. We prove that our method converges $R$-linearly in expectation, addressing an open problem in the literature related to designing theoretically supported adaptive SHBM methods. Numerical experiments show that our adaptive stochastic extended iterative method has strong advantages over the non-adaptive one.

math.NA↗

arXiv2025

A simple linear convergence analysis of the randomized reshuffling Kaczmarz method

The random reshuffling Kaczmarz (RRK) method enjoys the simplicity and efficiency in solving linear systems as a Kaczmarz-type method, whereas it also inherits the practical improvements of the stochastic gradient descent (SGD) with random reshuffling (RR) over original SGD. However, the current studies on RRK do not characterize its convergence comprehensively. In this paper, we present a novel analysis of the RRK method and prove its linear convergence towards the unique least-norm solution of the linear system. Furthermore, the convergence upper bound is tight and does not depend on the dimension of the coefficient matrix.

math.NA↗

arXiv2025

Enhanced randomized Douglas-Rachford method: Improved probabilities and adaptive momentum

Randomized iterative methods have gained recent interest in machine learning and signal processing for solving large-scale linear systems. One such example is the randomized Douglas-Rachford (RDR) method, which updates the iterate by reflecting it through two randomly selected hyperplanes and taking a convex combination with the current point. In this work, we enhance RDR by introducing improved sampling strategies and an adaptive heavy-ball momentum scheme. Specifically, we incorporate without-replacement and volume sampling into RDR, and establish stronger convergence guarantees compared to conventional i.i.d. sampling. Furthermore, we develop an adaptive momentum mechanism that dynamically adjusts step sizes and momentum parameters based on previous iterates, and prove that the resulting method achieves linear convergence in expectation with improved convergence bounds. Numerical experiments demonstrate that the enhanced RDR method consistently outperforms the original version, providing substantial practical benefits across a range of problem settings.

math.NA↗

arXiv2025

Connecting randomized iterative methods with Krylov subspaces

Randomized iterative methods, such as the randomized Kaczmarz method, have gained significant attention for solving large-scale linear systems due to their simplicity and efficiency. Meanwhile, Krylov subspace methods have emerged as a powerful class of algorithms, known for their robust theoretical foundations and rapid convergence properties. Despite the individual successes of these two paradigms, their underlying connection has remained largely unexplored. In this paper, we develop a unified framework that bridges randomized iterative methods and Krylov subspace techniques, supported by both rigorous theoretical analysis and practical implementation. The core idea is to formulate each iteration as an adaptively weighted linear combination of the sketched normal vector and previous iterates, with the weights optimally determined via a projection-based mechanism. This formulation not only reveals how subspace techniques can enhance the efficiency of randomized iterative methods, but also enables the design of a new class of iterative-sketching-based Krylov subspace algorithms. We prove that our method converges linearly in expectation and validate our findings with numerical experiments.

math.NA↗

arXiv2025

Randomized iterative methods for generalized absolute value equations: Solvability and error bounds

Randomized iterative methods, such as the Kaczmarz method and its variants, have gained growing attention due to their simplicity and efficiency in solving large-scale linear systems. Meanwhile, absolute value equations (AVE) have attracted increasing interest due to their connection with the linear complementarity problem. In this paper, we investigate the application of randomized iterative methods to generalized AVE (GAVE). Our approach differs from most existing works in that we tackle GAVE with non-square coefficient matrices. We establish more comprehensive sufficient and necessary conditions for characterizing the solvability of GAVE and propose precise error bound conditions. Furthermore, we introduce a flexible and efficient randomized iterative algorithmic framework for solving GAVE, which employs randomized sketching matrices drawn from user-specified distributions. This framework is capable of encompassing many well-known methods, including the Picard iteration method and the randomized Kaczmarz method. Leveraging our findings on solvability and error bounds, we establish both almost sure convergence and linear convergence rates for this versatile algorithmic framework. Finally, we present numerical examples to illustrate the advantages of the new algorithms.

math.NA↗

arXiv2025

Randomized block Kaczmarz with volume sampling: Momentum acceleration and efficient implementation

The randomized block Kaczmarz (RBK) method is a widely utilized iterative scheme for solving large-scale linear systems. However, the theoretical analysis and practical effectiveness of this method heavily rely on a good row paving of the coefficient matrix. This motivates us to introduce a novel block selection strategy to the RBK method, called volume sampling, in which the probability of selection is proportional to the volume spanned by the rows of the selected submatrix. To further enhance the practical performance, we develop and analyze a momentum variant of the method. Convergence results are established and demonstrate the notable improvements in convergence factor of the RBK method brought by the volume sampling and the momentum acceleration. Furthermore, to efficiently implement the RBK method with volume sampling, we propose an efficient algorithm that enables volume sampling from a sparse matrix with sampling complexity that is only logarithmic in dimension. Numerical experiments confirm our theoretical results.

math.NA↗

arXiv2024

ModelGrow: Continual Text-to-Video Pre-training with Model Expansion and Language Understanding Enhancement

Text-to-video (T2V) generation has gained significant attention recently. However, the costs of training a T2V model from scratch remain persistently high, and there is considerable room for improving the generation performance, especially under limited computation resources. This work explores the continual general pre-training of text-to-video models, enabling the model to "grow" its abilities based on a pre-trained foundation, analogous to how humans acquire new knowledge based on past experiences. There is a lack of extensive study of the continual pre-training techniques in T2V generation. In this work, we take the initial step toward exploring this task systematically and propose ModelGrow. Specifically, we break this task into two key aspects: increasing model capacity and improving semantic understanding. For model capacity, we introduce several novel techniques to expand the model size, enabling it to store new knowledge and improve generation performance. For semantic understanding, we propose a method that leverages large language models as advanced text encoders, integrating them into T2V models to enhance language comprehension and guide generation results according to detailed prompts. This approach enables the model to achieve better semantic alignment, particularly in response to complex user prompts. Extensive experiments demonstrate the effectiveness of our method across various metrics. The source code and the model of ModelGrow will be publicly available.

cs.CV↗

arXiv2024

Large Motion Video Autoencoding with Cross-modal Video VAE

Learning a robust video Variational Autoencoder (VAE) is essential for reducing video redundancy and facilitating efficient video generation. Directly applying image VAEs to individual frames in isolation can result in temporal inconsistencies and suboptimal compression rates due to a lack of temporal compression. Existing Video VAEs have begun to address temporal compression; however, they often suffer from inadequate reconstruction performance. In this paper, we present a novel and powerful video autoencoder capable of high-fidelity video encoding. First, we observe that entangling spatial and temporal compression by merely extending the image VAE to a 3D VAE can introduce motion blur and detail distortion artifacts. Thus, we propose temporal-aware spatial compression to better encode and decode the spatial information. Additionally, we integrate a lightweight motion compression model for further temporal compression. Second, we propose to leverage the textual information inherent in text-to-video datasets and incorporate text guidance into our model. This significantly enhances reconstruction quality, particularly in terms of detail preservation and temporal stability. Third, we further improve the versatility of our model through joint training on both images and videos, which not only enhances reconstruction quality but also enables the model to perform both image and video autoencoding. Extensive evaluations against strong recent baselines demonstrate the superior performance of our method. The project website can be found at~\href{https://yzxing87.github.io/vae/}{https://yzxing87.github.io/vae/}.

cs.CV↗

arXiv2024

A distributed Douglas-Rachford splitting method for solving linear constrained multi-block weakly convex problems

In recent years, a distributed Douglas-Rachford splitting method (DDRSM) has been proposed to tackle multi-block separable convex optimization problems. This algorithm offers relatively easier subproblems and greater efficiency for large-scale problems compared to various augmented-Lagrangian-based parallel algorithms. Building upon this, we explore the extension of DDRSM to weakly convex cases. By assuming weak convexity of the objective function and introducing an error bound assumption, we demonstrate the linear convergence rate of DDRSM. Some promising numerical experiments involving compressed sensing and robust alignment of structures across images (RASL) show that DDRSM has advantages over augmented-Lagrangian-based algorithms, even in weakly convex scenarios.

math.OC↗